Constant Envelope Orthogonal Frequency Division Research Articles

Constant Envelope Orthogonal Frequency Division Multiplexing With Index Modulation

Constant Envelope Orthogonal Frequency Division Multiplexing With Index Modulation

On the BER Performance of Constant Envelope OFDM in Frequency Selective MIMO Channels With ML Detection

In this contribution, we investigate the issue of constant envelope orthogonal frequency-division multiplexing (CE-OFDM) transmission in multipath fading channels, by quantifying its bit-error rate (BER) performance with the aid of maximum likelihood (ML) detection in multiple-input multipleoutput (MIMO) configurations. Through theoretical derivation, we demonstrate the advantage of CE-OFDM over its traditional counterparts as original OFDM and discrete Fourier transformspread-OFDM (DFT-s-OFDM) in terms of BER performance, which is ultimately supported by the simulation results.

Phase-Domain Injected Training for Channel Estimation in Constant Envelope OFDM

Constant envelope orthogonal frequency division multiplexing (CE-OFDM) is a multi-carrier waveform with 0 dB peak-to-average power ratio (PAPR). This property enables the exploitation of multi-carrier waveforms with non-linear power amplifiers, avoiding the undesirable clipping effects. However, the existing channel estimation techniques designed for OFDM cannot be reused, since the use of a phase modulator makes CE-OFDM a non-linear waveform. Previous works assumed that the channel estimation process relies on the transmission of preambles, and the data symbols are equalized using a frequency domain equalizer (FDE). To avoid the overhead induced by preambles, a phase-domain injected training (PIT) is proposed, where the pilot sequence is embedded in the phase dimension of the data symbols. This novel approach does not waste time and/or frequency resources as in preamble-based schemes. Moreover, it does not require additional power for the training. The received symbols are averaged with a dual procedure, and owing to the particular structure of CE-OFDM, the channel estimates are recovered. Also, the analytical expression of the channel estimation mean squared error (MSE) is derived. Finally, several numerical results illustrate the performance of the proposal, showing that the MSE, bit error rate (BER) and achievable rate are improved, as compared to the existing works.

Efficient LLR Approximation for Coded Constant Envelope OFDM

Constant envelope orthogonal frequency division multiplexing (CE-OFDM) is a promising technique to address the problem of high peak-to-average power ratio (PAPR) by embedding information into the phases of carriers since it was proposed. Meanwhile, in order to further enhance the bit error rate (BER) performance when using forward error correction (FEC) coding, the soft decision should be employed in CE-OFDM systems. However, due to the nonlinear noise in the phase of CE-OFDM, inaccurate log-likelihood ratios (LLRs) cause degradation of the decoding performance. To alleviate this problem, the systematic cause analysis of the phase noise is conducted followed by an efficient phase-noise oriented (PNO) algorithm for the phase demodulator in the CE-OFDM system. We further propose another stationary region Max-log-MAP (SR-MLM) algorithm with the phase unwrapper towards low implementation costs. Simulation results demonstrate that the proposed LLR approximation algorithms are capable of improving the BER performance of coded CE-OFDM compared to its conventional counterpart.

Constant envelope OFDM transmission over metro-regional optical links

The transmission of constant envelope orthogonal frequency division multiplexing (CE-OFDM) signals is experimentally demonstrated in this paper to increase the reach of metro-regional optical links. A recirculating fiber loop was implemented for this aim. A reach extension of 100 km of standard single-mode fiber was achieved with the CE-OFDM-based system, considering 16 quadrature amplitude modulation (16-QAM) as subcarrier mapping and links without optical dispersion compensation. Link lengths as long as 700 km, with spectral efficiency of 1.89 b/s/Hz, were accomplished with performances below the forward error correction limit.

Increasing the reach of visible light communication links through constant-envelope OFDM signals

The transmission of constant-envelope orthogonal frequency division multiplexing (CE-OFDM) signals, based on electrical phase modulation, was shown to improve the tolerance to noise and the nonlinearity introduced by light-emitting diodes (LEDs) in visible light communication (VLC) systems. This allows the application of larger signal amplitudes despite the LED-nonlinearities and, thus, data transmission over larger distances. The performance of a 9.51 Mb/s CE-OFDM based system, with 16-QAM subcarrier mapping in a bandwidth of 5 MHz, was compared to the efficiency of a conventional OFDM system. The error vector magnitude (EVM) was reduced from 17.5% to 10% (which is below the FEC limit), an improvement around 43%, when the CE-OFDM scheme was applied in the VLC link of 6 m. A good performance was achieved by the CE-OFDM based VLC system in a link of 8 m, when 4-QAM was used as subcarrier mapping.

Constant-Envelope OFDM for Power-Efficient and Nonlinearity-Tolerant Heterodyne MMW-RoF System With Envelope Detection

The radio over fiber (RoF) system using optical heterodyne (OH) for broadband up-conversion and envelope detection (ED) for phase-noise-insensitive down-conversion stands out as a simple, robust, and cost-effective solution for exploiting the abundant bandwidth resource at the millimeter-wave (MMW) band. In this paper, we dedicate efforts to experimentally investigate such an MMW-RoF system based on the constant-envelope orthogonal frequency division multiplexing (OFDM) (CE-OFDM) technique. A critical benefit of employing CE-OFDM is its excellent tolerance to the nonlinear distortions, which are essential for the wide acceptance of analog RoF systems. Also, thanks to the analog angle modulation transforming the OFDM signal to a constant envelope signal, the carrier-suppressed double-sideband (CS-DSB) modulation can be implemented for encoding the CE-OFDM signal onto the optical carrier, leading to significant improvements in power efficiencies of both fiber and radiofrequency (RF) links. In experiments, a 60-GHz OH-ED MMW-RoF system is established, of which the distances of fiber and MMW wireless transmissions are 10 km and 1.2 m respectively. Under the case of 2-GHz 64-quadrature amplitude modulation (QAM) OFDM baseband signal, the achieved experimental results show that the proposed OH-ED MMW-RoF system outperforms its counterpart using the conventional OFDM in terms of nonlinearity insensitivity, RF and optical power efficiency enhancements (indicated by over 11.5-dB and 3.2-dB reductions in the lowest transmit RF and receive optical powers for satisfying the 8% error-vector-magnitude (EVM) limit). In addition, when the QAM order of the 2.5-GHz OFDM baseband signal reaches 256, the CS-DSB CE-OFDM scheme enables an acceptable EVM performance of 4.43%.

Closed-Form Expression for BER of CE-OFDM in Optical Intensity-Modulated Direct-Detection Systems

A closed-form expression for the bit-error-rate (BER) of constant envelope orthogonal frequency division multiplexing (CE-OFDM) in intensity-modulated direct-detection optical systems is provided in this letter. To the best of our knowledge, this letter is the first that provides an expression of the BER that considers the impact of electrical phase modulation index, signal bandwidth, optical modulation index, and Mach–Zehnder modulator bias point. Simulation and experimental results are included to validate the accuracy of the expression, subject to an analysis of the impact of electrical phase modulation index and the level of subcarrier mapping. With the analytical expression, we are able to reduce the computation time in design and parameter optimization of optical systems based in the CE-OFDM.

Multiuser Equalizer for Hybrid Massive MIMO mmWave CE-OFDM Systems

This paper considers a multiuser broadband uplink massive multiple input multiple output (MIMO) millimeter-wave (mmWave) system. The constant envelope orthogonal frequency division multiplexing (CE-OFDM) is adopted as a modulation technique to allow an efficient power amplification, fundamental for mmWave based systems. Furthermore, a hybrid architecture is considered at the user terminals (UTs) and base station (BS) to reduce the high cost and power consumption required by a full-digital architecture, which has a radio frequency (RF) chain per antenna. Both the design of the UT’s precoder and base station equalizer are considered in this work. With the aim of maximizing the beamforming gain between each UT and the BS, the precoder analog coefficients are computed as a function of the average angles of departure (AoD), which are assumed to be known at the UTs. At the BS, the analog part is derived by assuming a system with no multi-user interference. Then, a per carrier basis nonlinear/iterative multi-user equalizer, based on the iterative block decision feedback equalization (IB-DFE) principle is designed, to explicitly remove both the multi-user and residual inter carrier interferences, not tackled in the analog part. The equalizer design metric is the sum of the mean square error (MSE) of all subcarriers, whose minimization is shown to be equivalent to the minimization of a weighted error between the hybrid and the full digital equalizer matrices. The results show that the proposed hybrid multi-user equalizer has a performance close to the fully digital counterpart.

Data-Aided Frequency Offset Estimation for CE-OFDM Broadband Satellite Systems

In recent years, the constant-envelope orthogonal frequency-division multiplexing (CE-OFDM) has been considered as a candidate waveform in broadband satellite systems as it has a 0-dB peak-to-average power ratio (PAPR). However, the carrier frequency offset (CFO) estimation scheme for CE-OFDM broadband satellite systems directly affects system performance. In this paper, we analyze the network architecture and the propagation environment of CE-OFDM broadband satellite systems, and we propose a data-aided CFO estimation strategy based on the frequency domain pilot symbols. The Cramer–Rao bound (CRB) of our CFO estimator is given by mathematical analysis, and the effect of the number of pilot symbols on the estimation performance is analyzed. The pilot symbol-based CFO estimator is composed of a phase demodulator and a discrete Fourier transform (DFT) module, and it can obtain a large estimation range under a small pilot overhead. The simulation results show that the CE-OFDM broadband satellite systems can achieve a good bit error rate (BER) performance by using the proposed strategy to estimate and compensate the CFO.

Waveform design for a dual‐function radar‐communication system based on CE‐OFDM‐PM signal

Owing to the exponentially increasing spectrum demand for commercial communication, radar and communication are increasingly encouraged to share spectrum. One approach is to incorporate information bearing communication sequences into radar waveforms. However, the varying radar/communication waveforms in a coherent processing interval lead to a range sidelobe modulation (RSM) that cause a loss of coherence when the Doppler processing operation is applied, thus leading to reduced target visibility. In this study, a new approach of embedding communication into radar waveform is proposed. Based on the scheme of constant envelope orthogonal frequency division multiplexing phase modulation (CE-OFDM-PM) and the orthogonality among trigonometric function, information bearing sequences are implemented using CE-OFDM-PM signal and then phase attached to a radar modulation term with a weighted coefficient. Also, the radar modulation term is synthesised by multiple sinusoidal functions where the coefficients of each sinusoidal modulation function are generated using random variables to achieve a thumbtack-like ambiguity function. The weighted coefficient of a communication modulation term provides a direct control of the degree of RSM. Theoretic analysis and simulation results show that a satisfactory communication bit error rate performance can be achieved without sacrificing the radar performance.

Constant-Envelope Multicarrier Waveforms for Millimeter Wave 5G Applications

A key point of Fifth Generation (5G) wireless networking will be the exploitation of higher frequency bands in the millimeter wave (mm-Wave) spectrum to provide unprecedented data rates to mobile users. In such a perspective, the PHYsical (PHY) layer design priorities should be reconsidered. In this paper, we investigate Constant-Envelope Multicarrier (CE-MC) waveforms for future adoption in mm-Wave 5G transmissions, namely: Constant-Envelope Orthogonal Frequency Division Multiplexing (CE-OFDM) and Constant-Envelope Single-Carrier OFDM (CE-SC-OFDM). These waveforms are obtained by imposing a nonlinear phase modulation to a real-valued OFDM and SC-OFDM signal, respectively. Thanks to their 0dB Peak-to-Average-Power Ratio, such unconventional signaling formats are insensitive to nonlinear distortions and allow to exploit the flexibility of conventional multicarrier systems together with augmented resilience against multipath fading and phase noise. CE-OFDM and CE-SC-OFDM have been assessed by means of computer simulations in a short-range mm-Wave 5G scenario, i.e., downlink transmission in outdoor picocells. Simulation results demonstrate that CE multicarrier waveforms enhance robustness and increase coverage and capacity in the proposed scenario, as compared to conventional OFDM and SC-OFDM counterparts.

Spectrum Efficiency Improvement for Quasi-Constant Envelope OFDM

Benefiting from low peak-to-average power ratio, constant envelope orthogonal frequency division multiplexing (CE-OFDM) is a promising technique in coherent optical communication. However, the spectrum efficiency of CE-OFDM is only half of the conventional coherent optical OFDM, which restricts its application. We proposed a novel quasi-CE-OFDM scheme with in-phase/quadrature modulator. Furthermore, a phase demodulation scheme based on Taylor series expansion is performed to reduce calculation complexity and avoid phase ambiguity. Simulation results show that the proposed scheme could double the spectrum efficiency effectively without losing the advantage of high nonlinearity tolerance.

Investigation into constant envelope orthogonal frequency division multiplexing for polarization-division multiplexing coherent optical communication

Benefiting from the high spectral efficiency and low peak-to-average power ratio, constant envelope orthogonal frequency division multiplexing (OFDM) is a promising technique in coherent optical communication. Polarization-division multiplexing (PDM) has been employed as an effective way to double the transmission capacity in the commercial 100 Gb/s PDM-QPSK system. We investigated constant envelope OFDM together with PDM. Simulation results show that the acceptable maximum launch power into the fiber improves 10 and 6 dB for 80- and 320-km transmission, respectively (compared with the conventional PDM OFDM system). The maximum reachable distance of the constant envelope OFDM system is able to reach 800 km, and even 1200 km is reachable if an ideal erbium doped fiber amplifier is employed.

Iterative Detection With Amplitude-Phase Demodulator For Dual-Stream CE-OFDM

Dual-stream constant envelope orthogonal frequency division multiplexing (CE-OFDM) is a flexible waveform that can achieve low peak-to-average power ratio and high spectral efficiency. In this letter, a receiver with iterative detection based on amplitude-phase demodulator is proposed for the demodulation of the dual-stream CE-OFDM. Simulation results show that iterative detection with amplitude-phase demodulator outperforms the existing receiver for dual-stream CE-OFDM, especially for high phase-modulation index and high-order modulation constellation.

Frequency offset compensation for satellite communication system with CE-OFDM

Constant envelope orthogonal frequency division multiplexing (CE-OFDM) is a waveform that can achieve 0dB peak-to-average power ratio and avoid the signal distortion caused by the nonlinear power amplifier. However, the carrier frequency offset (CFO) in CE-OFDM systems can cause errors at phase unwrapper module. In this paper, a CFO estimation scheme is proposed for CE-OFDM in satellite communication system. As the null subcarrier is inherent in the conjugate symmetric symbol structure at the transmitter, the proposed scheme uses the null subcarrier as prior information to estimate the CFO at the receiver. The ideal estimation range of normalized CFO is obtained by mathematical analysis. Simulation results show that the proposed scheme can estimate the CFO accurately under additive white Gaussian noise (AWGN) channel and multipath fading channel, especially for moderate and high signal-to-noise ratio (SNR).

Performance evaluation of CO-OFDM systems based on electrical constant-envelope signals

Abstract The influence of the electrical phase modulation index h in the performance of constant-envelope orthogonal frequency division multiplexing (CE-OFDM) in coherent detection optical systems is treated analytically and its range of validity examined by simulations. A compromise between h and subcarrier mapping is identified according to differences in sensitivity related to non-linearities inserted by the optical modulator. It is shown that the proposed scheme outperforms conventional coherent detection OFDM systems, which is strongly dependent on both phase and optical modulation indexes.

CE-OFDM Schemes: Spectral Characterization and Optimum Performance

Constant envelope orthogonal frequency division multiplexing (CE-OFDM) techniques have been recently proposed to allow the use of power-efficient saturated amplifiers, since those signals do not have the high peak-to-average ratio of OFDM signals, but maintain most of the OFDM advantages. However, the nonlinear nature of the phase modulation process inherent to CE-OFDM schemes gives rise to both theoretical challenges (analytical difficulties due to the nonlinear processes involved) and practical challenges (spectral widening and possible performance degradation due to nonlinear distortion effects). In this work, we present accurate expressions for the average power spectral density of CE-OFDM signals. Making use of recent results that indicate performance gains associated to the optimum detection of nonlinearly distorted multicarrier signals, we also investigate the optimum detection of CE-OFDM signals considering both additive white Gaussian noise channels and frequency-selective channels with Rayleigh fading, providing theoretical expressions for the asymptotic gains as well as the correspondent approximate bit-error-rate results.

Constant Envelope Phase Modulation Inspired by Orthogonal Waveforms

Constant envelope orthogonal frequency division multiplexing (CE-OFDM) is a technique to modify the OFDM signal with high peak-to-average power ratio (PAPR) to a constant envelope zero decibel PAPR waveform. The conventional CE-OFDM uses inverse discrete Fourier transform to calculate the signal time samples before feeding them to the phase modulator. This letter describes a different approach for the implementation of a constant envelope of generating phase digitally modulated waveforms that may be easier for implementation. The new approach, which we termed “constant envelope $M$ -ary time orthogonal” (CE-MTO), is based on orthogonal waveforms in the time domain. A time domain-analytical study of the CE-MTO in the presence of an additive white Gaussian noise is presented. Simulations of the CE-MTO performances show the comparable results to those of the CE-OFDM technique also in a frequency selective channel.

On the Detection of CE-OFDM Signals

In this letter, we study the optimum performance of constant envelope orthogonal frequency division multiplexing (CE-OFDM) signals in both ideal additive white Gaussian noise channels and frequency-selective channels, and we compare it to the performance of conventional CE-OFDM receivers based on a phase detector. It is shown that the phase detector can achieve optimum performance, but only in scenarios where the power efficiency is very low. For this reason, the use of CE-OFDM schemes in power-constrained scenarios may demand other type of receivers, such as optimum-based receivers.